The nonlinear digital filtering methods which are based on threshold decomposition and positive Boolean functions are becoming widely used. They are in use especially in image processing and biomedical signal processing, both of which usually involve large amounts of data. It is thus important to develop fast algorithms to realize weighted median weighted order statistics and more general stack filtering operations. The amounts of data are so large that fast algorithms are needed no matter how powerful the computers are that are available. In the following paper we introduce new algorithms for some of these problems and discuss the use of logical matrix algorithms for the solution of nonlinear digital filtering problems.